An environmental dose experiment

Living beings are exposed to natural radiation sources. The main natural sources of exposure are cosmic radiation and natural radionuclides found in the soil and in rocks. At ground level, muons (with energy in the range 1 to 20 GeV) constitute the dominant component of the cosmic ray field. Gamma photons are on the other hand the major contributor to dose due to radionuclides. Effective doses may vary from place to place but usually are in the range of 1 to 10 mSv/a [1], with an average at 2.4 mSv/a. According to a UNSCEAR 2008 report [2], low-ionizing density radiation is responsible for an estimated 0.48 mSv/a from external terrestrial radiation to the body and 0.39 mSv/a from cosmic radiation (world average). We should note that these estimates have changed throughout the years and different sources quote different values.

The measurement of the environmental dose due to cosmic ray and gamma ray sources can be made using a plastic scintillation detector. In this work we describe the operation of a plastic scintillation detector used as an environmental dosimeter, assessing the annual dose delivered in the laboratory. The detector was built in our laboratory by students as part of a research project.

The environmental dose is due to weak sources and measurements are usually made by detectors with sufficiently large volumes. A popular choice is plastic scintillation detectors. Compared to scintillation inorganic crystals, plastic scintillators have a much lower price per unit volume. On the physical side, plastics have much better equivalence to water than inorganic crystals. When translating the dose D_m delivered by photons at the dosimeter material to dose D_w at water (or organic tissue), the conversion factor is the ratio of average mass absorption coefficients $\overline{{\mu }_{en}/\rho }$ [3, 4]

$$\begin{eqnarray}&&{D}_{w}={D}_{m}\overline{{({\mu }_{en}/\rho )}_{m}}/\overline{{({\mu }_{en}/\rho )}_{w}}.\end{eqnarray} \tag{ 1 }$$

The average value must be obtained over the relevant photon fluence spectrum [5], the details of which may be largely unknown for natural sources. If the ratio of mass absorption coefficients is approximately constant over that range, knowledge of the spectrum is no longer relevant. This is the case of some plastics like PMMA, polystyrene or PVT as it can be checked using data from the NIST website [6]. In table 1 the ratio of mass absorption coefficients of these plastics to water is presented.

Table 1.  Approximate ratio of mass absorption coefficients of plastics to water in the 0.3 to 4 MeV range. The ratio for 1.25 MeV is presented. Mass absorption coefficients were obtained from [6].

	PMMA	Polystyrene	PVT
${({\mu }_{en}/\rho )}_{m}/{({\mu }_{en}/\rho )}_{w}$	0.9376	0.9693	0.9761

For charged particles equation (1) doesn't apply and the relevant conversion factor is given by the mass stopping power $\overline{(S/\rho )}$ coefficients ratio [3, 4]

$$\begin{eqnarray}&&{D}_{w}={D}_{m}\overline{{(S/\rho )}_{m}}/\overline{{(S/\rho )}_{w}}.\end{eqnarray} \tag{ 2 }$$

The main component of cosmic rays reaching the Earth's surface is due to high-energy muons with energies in excess of 1 GeV [7]. These particles are often refereed to as minimum ionizing particles (MIPs), since their stopping power is approximately equal to the minimum value obtained from the Bethe-Bloch curve [7]. The ratio of mass stopping power coefficients of plastics to water for minimum ionizing particles is presented in table 2.

Table 2.  Ratio of mass stopping power coefficients of plastics to water for minimum ionizing particles [7].

	PMMA	Polystyrene	PVT
${(S/\rho )}_{m}/{(S/\rho )}_{w}$	0.9684	0.9719	0.9819

Our detector's sensitive volume is a cylinder, 4.60 cm in diameter and 10.00 cm long, made of a PMMA scintillator (RP-200A [8]). The scintillator is coupled with optical grease to a 2 inch PMT (Hamamatsu R6231). The scintillator is wrapped in Tyvek™ white paper for better light collection. The ensemble was enclosed in a PVC case with 8 mm-thick walls. The signal from the detector was fed to a NIM amplifier and collected by a multichannel analyser. To calibrate the detector, radioactive sources (¹³⁷Cs, ⁶⁰Co and ²²Na) were used. The sources' activity were measured in our laboratory using a 3'' × 3'' NaI(Tl) detector following the procedure in [9]. The measured values are presented in table 3.

To obtain the deposited energy in the detector per disintegration, a Monte Carlo simulation of the setup was made using Penelope [11–13]. Penelope simulates the transport of electrons, photons and positrons through matter in a wide energy range (250 eV to 1 GeV). The cylindrical geometry of the detector enables the use of a pencyl routine with a less complicated geometry interface than the standard penmain routine [11]. A full description of the detector (scintillator and detector wall) was made. Point-like radioactive sources, placed at chosen distances, were simulated (one distance at a time). For each radioactive source, the relevant photon spectrum was considered (see table 4). The program is designed to generate and track one primary particle per event, while on average more than one photon can be emitted per event in most cases. One way to correctly account for all deposited energy is to separately simulate each photon and add-up each contribution weighted by the photon's percentage per disintegration. While one should consider isotropic sources, and thus 4π photon emission, for the two 511 keV annihilation photons, only one photon should be simulated in a 2π emission and thus increasing its weight by a factor of 2. The program output will be the deposited energy in the detector sensitive volume per event (or per disintegration). The dose is computed as the ratio of the deposited energy to the scintillator mass. Considering a density of 1.19 g cm⁻³ for PMMA [8], the mass of our scintillator is (0.198 ± 0.001) kg. The experiment's final result will critically depend on the accuracy of the Monte Carlo simulation. In most cases the best way to assess the quality of the simulation is to compare simulated results with experiment. An experiment using a low-activity, large solid angle ⁴⁰K source was designed for this purpose. A comparison between simulated and measured dose is made, providing a cross check for the method.

Plastic scintillation detectors have poor energy resolution [15], as demonstrated in the spectrum of figure 1 obtained with our detector for a ¹³⁷Cs source. The gamma background spectrum presents a similar shape (i.e. no peaks are present) although extended to higher energy (see figure 3). Both low density and moderate light yield (when compared to inorganic scintillation crystals) contribute to this outcome. However for dosimetry this is not a serious disadvantage, since the measurement doesn't rely on single photon detection but rather on the integration of the energy over a number of events. Thus, it is important to maintain signal-energy proportionality, but not on an event basis.

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In this experiment the signal S is obtained as the sum of the product of the multichannel analyser (mca) channel ch (proportional to single event energy) by the number of counts in that channel, in a given channel range, averaged over an acquisition time T, i.e.

$$\begin{eqnarray}&&S=\tfrac{1}{T}\displaystyle \sum _{c{h}_{\min }}^{c{h}_{\max }}(ch\times counts).\end{eqnarray} \tag{ 3 }$$

The choice of the lower threshold channel ch_min depends on electronic background noise. The evaluation of this threshold is crucial for the environmental dose determination since electronic and natural backgrounds are mixed. Once the threshold is set, the calibration of the detector can be made. Figure 2 displays dose per disintegration versus signal for a set of measurements with each of the radioactive sources placed at different distances from the detector. A linear relation between the two variables is observed over several orders of magnitude, which is a remarkable result.

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It is a well-established fact that PMTs have a dark noise current [15], contributing to the low energy noise. After the detector's assemblage it is not easy to separate this noise from the background noise originated by natural radiation sources. An assessment of its importance in percentage and range can be made comparing the background spectra (i.e. without the presence of individual sources) obtained with the detector inside and outside a lead housing. For the task, a lead brick (5 cm thick) castle was built in such a way that the detector could be fully enclosed. In figure 3 is presented the result for the background spectra obtained with the detector outside and inside the lead castle. Analysing the ratio of the two spectra, two distinct regions can be established: a low energy region with growing ratio values, and a fairly constant ratio region above the threshold channel.

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The low energy gamma background is greatly reduced by the lead shield, so in the low channel range the contribution of electronic noise to the spectrum is enhanced. As energy increases so does the percentage of radiation penetrating the shielding. For high enough channel values the contribution of electronic noise to the background (which is not affected by the lead shielding) is greatly reduced and the ratio tends to be fairly constant. A threshold was then arbitrarily set at the channel with 90% of the maximum ratio value (corresponding to channel 30 in our case). A relative difference of 3% is observed in the overall ratio (i.e. the ratio of the spectra integrals) when the threshold is moved five channels (left or right). The threshold ensures a considerable reduction in the electronic noise contribution at the expense of cutting the contribution of low energy radiation to the measured dose value. The background signal eliminated by this cut was approximately 20% of the total measured background signal. This 20% includes electronic noise background as well as background signal due to low energy deposits in the detector from gammas and muons.

A simple straight line fit was applied to the data in figure 2. A slope of $(3.02\,\pm \,0.04)\times {10}^{-9}$ μGy/s and an intercept of $(2.9\,\pm \,1.7)\times {10}^{-6}$ μGy/s were obtained for our setup.

Muons from the pion decay, produced in the collisions of primary cosmic ray particles, have an average energy of the order of 3 GeV at ground level [7, 16] and can be considered as minimum ionizing particles (MIPs) [7, 17]. Since the stopping power $dE/dx$ is a slow varying function of the particle energy for MIPs, the energy loss ΔE in thin slabs can be approximated by

$$\begin{eqnarray}&&{\rm{\Delta }}E=\left(-\tfrac{dE}{dx}\right){\rm{\Delta }}x,\end{eqnarray} \tag{ 4 }$$

where ${\rm{\Delta }}x$ is the thickness of the slab. For this purpose a slab can be considered as 'thin' for a particle of energy E if ${\rm{\Delta }}E\ll E.$ The mass stopping power for MIPs for PMMA is 1.929 MeV cm²g⁻¹ [18]. Since the density of PMMA is 1.19 g cm⁻³, a muon traversing the full length of the detector (10 cm) will then lose an energy amount of ${\rm{\Delta }}E=\mathrm{1.929\; \times \; 1.19\; \times \; 10}\,\approx \,23\,{\rm{MeV}}.$ We can thus expect to have a muon contribution to the spectrum up to high energy. Furthermore, it is known [15] that the amount of scintillation light produced per deposited MeV is different for electrons (or gammas) and heavier particles. The calibration made using gamma sources is thus not applicable to extract the muon contribution to the dose. To our knowledge, there is no published work on the scintillation light produced by muons on the RP-200A scintillator. A separation of the muon signal component from the gamma is thus necessary.

To do so, information on the percentage of each radiation component is needed. That information cannot be obtained directly from the detector. However, the detected gamma component can be decreased to a negligible level by shielding the detector with lead bricks. A 5 cm lead brick will attenuate the gamma component by ${e}^{-5\mu },$ where $\mu$ is the linear attenuation coefficient in cm⁻¹. For ⁶⁰Co gamma photons the attenuation factor is about 0.036, being smaller for lower energy photons.

On the other hand, high-energy muons still reach the detector. In fact, using 1.122 MeV g⁻¹ cm² for the MIPs [7, 18] in lead, a value of approximately 64 MeV for the lost energy is obtained. Let then m and g be, respectively, the muon and gamma total signal above threshold as defined by equation (3). Assuming zero gamma contribution in the shielded scenario, one gets for the ratio r between shielded and unshielded cases

$$\begin{eqnarray}&&r=\displaystyle \frac{m}{m+g}\end{eqnarray} \tag{ 5 }$$

which is the muon fraction contribution for the signal. For our data $r=0.161\,\pm \,0.001$ (statistical uncertainty only).

The 30 channel threshold was applied to the background radiation spectrum and the signal obtained according to equation (3). Applying calibration to the gamma component (i.e. 83.9% of the signal), a value of $(1.64\,\pm \,0.02)$ μGy/s is obtained, corresponding to $(0.52\,\pm \,0.05)$ mGy for the time period of one year. This is the dose in PMMA. To convert dose in PMMA to dose in water, equation (1) should be applied. Using ${({\mu }_{en}/\rho )}_{pmma}/{({\mu }_{en}/\rho )}_{water}=0.9376$ from table 1, we arrive at $(0.48\,\pm \,0.05)\,{\rm{mGy}}$ for the dose in water. Only statistical uncertainties have been considered.

The detector was also tested on dose measurement of a known low-activity source. For this purpose potassium chloride (KCl) in powder was chosen. ⁴⁰K is a naturally occurring radioactive isotope of potassium in an abundance of 0.0117% and has an half-life of $1.277\times {10}^{9}$ year [10]. Potassium chloride can be purchased at high purity and exempt of any license. A cylindrical source weighing 3.040 kg was made. The source has a hole in its centre to accommodate the detector and its height was such that it encompassed the whole sensitive part of the detector. To compute the source activity, the following equation can be used [19]:

$$\begin{eqnarray}&&A=\tfrac{\mathrm{ln}(2)}{{T}_{\mathrm{1/2}}}\times \tfrac{{M}_{KCl}B}{{A}_{KCl}}\times {N}_{A}\end{eqnarray} \tag{ 6 }$$

where T_1/2 is the ⁴⁰K half-life, M_KCL the potassium chloride mass, B the ⁴⁰K abundance, A_KCl the molar mass of potassium chloride and N_A the Avogadro's constant. For our source an activity value of $(49.4\,\pm \,0.5)$ kBq was computed. The experimental setup (cylindrical KCl source and scintillation detector) was simulated with the Penelope program to obtain the dose per disintegration factor. For this purpose a density of $(0.93\,\pm \,0.02)$ g cm⁻³ was estimated, considering the measured weight and volume occupied by the KCl sample. A factor of $(0.960\,\pm \,0.003)$ keV/decay was obtained from simulation. To get the factor that translates activity to dose rate, we multiply by $1.602\times {10}^{-16}$ J keV⁻¹, converting keV to joule, and divide by the detector's mass. A factor of $(7.77\,\pm \,0.03)\times {10}^{-16}$ Gy/decay is then obtained. Using this factor and the computed source activity, a dose rate of $(3.84\,\pm \,0.03)\times {10}^{-11}$ Gy/s is expected. For the used KCl source, after background subtraction to the signal, computed according to equation (3), and using the previous signal to dose rate calibration, a corresponding dose rate of $(3.5\,\pm \,0.2)\times {10}^{-11}$ Gy/s was obtained, representing a difference of 9% to the computed value.

Background radiation is a constant presence everywhere. For most laboratory experiments it is just one more difficulty to deal with. In this work a plastic scintillator detector was used to estimate the annual dose due to background radiation. The measured dose rate value of 0.48 mGy/a is in the same range as the background dose due to gamma radiation from natural sources reported in international reports for Western Europe [2]. The same method was applied to the measurement of the dose delivered by a low-activity KCl cylindrical source. A difference of 9% between the computed and measured values was found, being a reasonable result given the overall uncertainties.

We are grateful to Laboratório de Instrumentação e Física Experimental de Partículas for the financial support given to this work. We are also grateful to Ashley Peralta for the review of the English text and to Prof. Jorge Sampaio for the critical reading of the document.